Find the value of the following fractional expression:
10/1 + 9/2 – 8/3 – 7/4 – 6/5 – 5/6 – 4/7 – 3/8 – 2/9 – 1/10
Provide your answer as a simplified fraction.
your lowest common denominator is
9*8*5*7 or 2520
take it from there
To find the value of the given fractional expression, you need to add and subtract the fractions in the expression.
First, let's rewrite the expression in a clearer form:
10/1 + 9/2 - 8/3 - 7/4 - 6/5 - 5/6 - 4/7 - 3/8 - 2/9 - 1/10.
To simplify the process, let's find a common denominator for all the fractions. The least common multiple (LCM) of the denominators is 2520. Therefore, we need to convert every fraction so that they all have a denominator of 2520.
10/1 = 2520/252
9/2 = 1260/252
8/3 = 840/252
7/4 = 630/252
6/5 = 504/252
5/6 = 420/252
4/7 = 360/252
3/8 = 315/252
2/9 = 280/252
1/10 = 252/252
Now, we can rewrite the expression with the common denominator:
2520/252 + 1260/252 - 840/252 - 630/252 - 504/252 - 420/252 - 360/252 - 315/252 - 280/252 - 252/252.
Next, we can combine the fractions:
(2520 + 1260 - 840 - 630 - 504 - 420 - 360 - 315 - 280 - 252) / 252.
Simplifying the numerator gives us:
-489 / 252.
Therefore, the value of the fractional expression is -489/252, which is already in simplified form.